It is given that the population of world in 1950 was about 2.556
billion and by 1980, it increased to about 4.458 billion.

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Step 2 of 5

It is required to write an exponential function that can be used
to model the world population
in billions for 1950 to 1980 where
is the number of years since 1950.

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Step 3 of 5

The exponential model is of type
whereis
the population in billions and
is the year. Let
be represents the year 1950. To form the required model, it is
required to find the value of constant.
The value of constant
will be given by initial condition as follows:

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Step 4 of 5

Similarly, the value of constant
will be given as follows:

Solving for,
it can be seen that

Since, the population is increasing over the years. So,
will be positive. Now, the required exponential model will be given
by

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Step 5 of 5

Hence, the required exponential model will be given by
where
is the population of the world in billions and
is the year in which
represents 1950.